Cleaning up after a messy diaper in public

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I need to know how to do this. A few days ago I was out of town walking in the Valley of the National park. Not really on a trail, but exploring the beauty of nature in the middle of nowhere. I was well protected for my bladder issues, and all of the sudden I needed to have a BM bad. This usually does not happen to me, and I was at least 20 minutes from home or a public bathroom which I hate to use anyhow. I opted to head back to my car and drive home. A few minutes into my drive home it was obvious I was not going to make it. I thought about the posts I read on here from others who daily use their diapers for everything so I figured what choice do I have. I relaxed in my car and used my diaper. when I got home I took it off, and tried to clean up but it was spread from my back to my front. I ended up having to shower off to clean up. I don't understand how some one can go into a public bathroom and change and clean up after a mess like this? I know this won't be the last time I end up having to use my diaper this way, and I would like to be able to get to a public bathroom, change and go back to enjoying my day. What am I missing or how do you do this? Thanks for your time.Bryan